Question: Divide the product of the first five positive composite integers by the product of the next five composite integers. Express your answer as a common fraction.
The first ten positive composite integers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. The desired quotient is $\frac{4\cdot6\cdot8\cdot9\cdot10}{12\cdot14\cdot15\cdot16\cdot18}$. After cancellation, we get $\frac{1}{14\cdot3}=\boxed{\frac{1}{42}}$.